Finite Group Databasebeta

← #25007281

Subgroups — #25007281

Order 11008.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#398×D43C211yesmaximal, characteristic
2#19134674C211yesmaximal, characteristic
3#19132923C211yesmaximal, characteristic
4#19132602C211yesmaximal, characteristic, complemented
5#19132601C211yesmaximal, characteristic, complemented
6#19132600C211yesmaximal, characteristic, complemented
7C43×#1346C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D43—21no—
9C2×C4⋊C4×D43C411yescharacteristic
10C2×C4⋊C4×D43C2211yescharacteristic
11#14582862—21no—
12#14582861—21no—
13#14582833—21no—
14#14582832—21no—
15#14582831C411yescharacteristic
16#14582830C411yescharacteristic
17#14582829C2211yescharacteristic
18#95×D43—21no—
19#95×D43C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#398C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43—21no—
28C22×C4×D43—21no—
29C22×C4×D43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C2×#10621877—21no—
33C2×#10621872—41no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4C2×C411yescharacteristic
41C2×Dic43⋊C4D411yescharacteristic
42C4⋊C4×D43—41no—
43C4⋊C4×D43—41no—
44C4⋊C4×D43—41no—
45C4⋊C4×D43—41no—
46C4⋊C4×D43—42no—
47C4⋊C4×D43—42no—
48C22⋊(C43⋊C8)—21no—
49(C2×D43)⋊C8—41no—
50(C2×D43)⋊C8—41no—
51(C2×D43)⋊C8—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C2×M16×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—24no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—41no—
85C2×C4×D43—42no—
86C2×C4×D43—42no—
87C2×C4×D43—42no—
88C2×C4×D43—42no—
89C2×C4×D43—42no—
90C2×C4×D43—42no—
91C2×C4×D43—41no—
92C2×C4×D43—41no—
93M16×C43—41no—
94M16×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊Dic43—41no—
102C4⋊Dic43—42no—
103C4⋊Dic43—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106Dic43⋊C4—42no—
107Dic43⋊C4—42no—
108Dic43⋊C4—41no—
109Dic43⋊C4—41no—
110#10621877—41no—
111#10621877—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114#10621872—82no—
115C23×C43C2×C22⋊C411yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—22no—
119C22×D43—22no—
120C22×D43#9911yescharacteristic
121C22×D43#9911yescharacteristic
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×Dic43—22no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C4×D43—41no—
150C4×D43—41no—
151C4×D43—41no—
152C4×D43—41no—
153C4×D43—48no—
154C4×D43—42no—
155C4×D43—42no—
156C4×D43—42no—
157C4×D43—81no—
158C4×D43—82no—
159C4×D43—82no—
160C8×C43—81no—
161C8×C43—81no—
162C43⋊C8—81no—
163C43⋊C8—81no—
164#11803—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43C2×#9911yescharacteristic
168C22×C43#41811yescharacteristic
169C22×C43#42111yescharacteristic
170C2×D43—24no—
171C2×D43—24no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—21no—
176C2×D43#35212yes—
177C2×D43#35612yes—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—42no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43—81no—
184Dic43—42no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188Dic43—81no—
189C2×#398—431no—
190#1821—431no—
191#1463—431no—
192#1346—431no—
193#1346—431no—
194#1346—431no—
195#1346D4311yescharacteristic, complemented
196C2×C43—21no—
197C2×C43—21no—
198C2×C43#151011yescharacteristic
199C2×C43C2×#35211yescharacteristic
200C2×C43C2×#35611yescharacteristic
201D43—22no—
202D43—22no—
203C22×C4⋊C4—431no—
204C22×C4⋊C4—431no—
205C22×C4⋊C4—861no—
206#407—861no—
207#407—861no—
208#398—431no—
209#398—431no—
210#398—431no—
211#398—861no—
212#398—861no—
213#398C2×D4311yescharacteristic
214C2×#95—431no—
215C2×#95—861no—
216#343—431no—
217#343—861no—
218#343C2×D4311yescharacteristic
219#324—431no—
220#324—861no—
221#324C2×D4311yescharacteristic
222C43#1180311yescharacteristic, complemented, Sylow
223C23×C4—431no—
224C23×C4—431no—
225C23×C4—431no—
226C23×C4—861no—
227C23×C4—861no—
228C2×M16—21no—
229C2×M16—861no—
230C2×M16—1721no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—1721no—
241C2×C4⋊C4—1721no—
242C2×C4⋊C4—1721no—
243C2×C4⋊C4—1721no—
244C2×C4⋊C4—1722no—
245C2×C4⋊C4—1722no—
246C2×C4⋊C4C4×D4311yescharacteristic
247C2×C4⋊C4C22×D4311yescharacteristic
248C22⋊C8—21no—
249C22⋊C8—861no—
250C22⋊C8—1721no—
251C22⋊C8—1721no—
252C22⋊C8—1721no—
253#95—21no—
254#95—431no—
255#95—861no—
256#95—861no—
257#95—861no—
258#95—861no—
259#95C4×D4311yescharacteristic
260C24—431no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—431no—
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—864no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4—1721no—
280C22×C4—1722no—
281C22×C4—1722no—
282C22×C4—1722no—
283C22×C4—1722no—
284C22×C4—1722no—
285C22×C4—1722no—
286C22×C4C2×C4×D4311yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289M16—41no—
290M16—41no—
291M16—3442no—
292M16—1721no—
293M16—1721no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—1721no—
297C2×C8—1721no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4—1721no—
305C4⋊C4—1721no—
306C4⋊C4—1722no—
307C4⋊C4—1722no—
308C4⋊C4—1722no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C23—431no—
312C23—431no—
313C23—862no—
314C23—862no—
315C23—861no—
316C23—861no—
317C23C22⋊C4×D4311yescharacteristic
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—862no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—3441no—
337C2×C4—3442no—
338C2×C4—3442no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1728no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4#1306334911yescharacteristic
355C2×C4#1306335211yescharacteristic
356C8—81no—
357C8—81no—
358C8—3441no—
359C8—3441no—
360C22—21no—
361C22—21no—
362C22—432no—
363C22—432no—
364C22—864no—
365C22—864no—
366C22—861no—
367C22—861no—
368C22—861no—
369C22—861no—
370C22#99×D4311yescharacteristic
371C22#1458290211yescharacteristic
372C22#1458291411yescharacteristic
373C4—21no—
374C4—21no—
375C4—42no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—3441no—
380C4—1722no—
381C4—1721no—
382C4—1721no—
383C4—1721no—
384C2—21no—
385C2—21no—
386C2—862no—
387C2—862no—
388C2#1913312211yescharacteristic
389C2#352×D4311yescharacteristic
390C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1346C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1346D43
hypocenterC43#11803
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #19132602C2semidirect
5. #19132601C2semidirect
6. #19132600C2semidirect
7. C43×#1346C2semidirect
195. #1346D43semidirect
222. C43#11803semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#398×D432
#191346742
#191329232
#191326022
#191326012
#191326002
C43×#13462
#1180343